Racetrack memories (RMs) are prone to alignment faults called position errors (PEs), which manifest as insertions and deletions of stored data bits. Conventional coding schemes for PEs demonstrate the promising results by employing low-density parity-check (LDPC) codes with an iterative detection and decoding algorithm. However, the computational complexity of detection is relatively high. In this article, for channels with PEs, we present a new coding scheme that can effectively decode corrupted data, even if the detection is executed only once (i.e., a non-iterative detection and decoding scenario). The proposed code consists of a concatenation of an inner 2-D marker code, which is specialized for PEs to mitigate the effect of insertion and deletion (ID) errors, and an outer irregular LDPC code. We also provide tractable design methodologies for these constituent codes. First, we identify the 2-D-marker code structures that offer higher achievable information rates in a non-iterative scenario and then optimize irregular LDPC codes to ensure good decoding properties. Through asymptotic-performance analysis and finite-length simulation, we confirm the effectiveness of the proposed coding scheme. Ultimately, the proposed coding scheme has the capability to reduce code rate loss and to provide excellent decoding performance under a non-iterative scenario, which also helps in understanding the reliability of RM when a low-complexity decoding algorithm is used to correct ID errors caused by PEs.

中文翻译：

---

用于恢复赛道记忆中位置误差的级联 LDPC/2D 标记码和非迭代检测/解码

Racetrack 存储器 (RM) 容易出现称为位置错误 (PE) 的对齐错误，这表现为存储数据位的插入和删除。传统的 PE 编码方案通过使用具有迭代检测和解码算法的低密度奇偶校验 (LDPC) 码证明了有希望的结果。但是检测的计算复杂度比较高。在本文中，对于具有 PE​​ 的信道，我们提出了一种新的编码方案，即使检测仅执行一次（即非迭代检测和解码场景），也可以有效解码损坏的数据。所提出的代码由内部二维标记代码和外部不规则 LDPC 代码的串联组成，该代码专用于 PE 以减轻插入和删除 (ID) 错误的影响。我们还为这些组成代码提供易于处理的设计方法。首先，我们确定在非迭代场景中提供更高可实现信息速率的二维标记代码结构，然后优化不规则的 LDPC 代码以确保良好的解码特性。通过渐近性能分析和有限长度仿真，我们证实了所提出的编码方案的有效性。最终，所提出的编码方案能够在非迭代场景下降低码率损失并提供出色的解码性能，这也有助于理解当使用低复杂度解码算法纠正由 ID 引起的错误时 RM 的可靠性。由 PE。我们确定了在非迭代场景中提供更高可实现信息率的二维标记码结构，然后优化不规则的 LDPC 码以确保良好的解码性能。通过渐近性能分析和有限长度仿真，我们证实了所提出的编码方案的有效性。最终，所提出的编码方案能够减少码率损失并在非迭代场景下提供出色的解码性能，这也有助于理解当使用低复杂度解码算法纠正由 ID 引起的错误时 RM 的可靠性。由 PE。我们确定了在非迭代场景中提供更高可实现信息率的二维标记码结构，然后优化不规则的 LDPC 码以确保良好的解码性能。通过渐近性能分析和有限长度仿真，我们证实了所提出的编码方案的有效性。最终，所提出的编码方案能够减少码率损失并在非迭代场景下提供出色的解码性能，这也有助于理解当使用低复杂度解码算法纠正由 ID 引起的错误时 RM 的可靠性。由 PE。